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Two blocks of mass m and M are connected via pulley with a configuration as sho…

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Wize University Physics Textbook (Master) > Newton's Laws of Motion: Forces and Dynamics

Tension

3 Activities

Wize University Physics Textbook (Master) > Newton's Laws of Motion: Forces and Dynamics

Inclined Surfaces

3 Activities

Two blocks of mass m and M are connected via pulley with a configuration as shown. The surfaces are frictionless. If M=15 kg and m=8 kg and θ1=30 and θ2=60\theta_1=30\ {\rm and}\ \theta_2=60
  1. Find the acceleration
  2. What is the tension in the string?

More Tension Questions:
Two blocks are connected by a light string which passes over two pulleys as shown. The string and the pulleys are massless and there is no friction. A scale located between two pulleys. The heavier block has a mass of 5kg, and the lighter block has a mess of 3kg. What is the reading on the scale (Pick the closest answer)
Two blocks of mass m and M are connected via pulley with a configuration as shown. The surfaces are frictionless. If M=15 kg and m=8 kg and θ1=30 and θ2=60\theta_1=30\ {\rm and}\ \theta_2=60
Find the acceleration
What is the tension in the string?
Two strings on a spinning rod - solving
Practice: Two Strings on Spinning Rod
The 4.00-kg block in the figure is attached to a vertical rod by means of two strings. When the system rotates about the axis of the rod, the strings are extended as shown in the diagram and the tension in the upper string is 80.0 N.
Suspended masses
Three masses are suspended from each other as shown. Assume they have equal masses (they are given numbers 1, 2, and 3 for identification purposes only). Which rope has the highest tension? Which has the lowest tension? Why?
Method of sections + example
Determine the forces F1, F2, F3 shown below. The structure is fixed at the left to a wall. All angles are either 45 or 90 degrees. Use positive numbers for members in tension and negative numbers for members in compression.
Practice: Two masses on a pulley
If M = 10kg and m = 5kg, find the net acceleration of the masses. Assume the pulley and strings are frictionless and of negligible mass.
A 5 kg5\ kgblock is being pulled along at table by a cable (horizontally) and is accelerating along the surface at 2[ms2]2\left[\frac{m}{s^2}\right]. The coefficient of kinetic friction between the block and the table is 0.100.10.
a) Sketch the system.
b) Find the tension in the cable.
Consider the truss shown below. (On the left is a sturdy wall.) All triangles are 45-45-90 triangles.
a) Label each member as either being in compression, in tension, or a zero force member.
b) Determine the value of F1, F2, and F3.
A 10 kg mass is hanging from a rope wrapped around a cylindrical pulley. The falling mass causes the pulley to rotate. The mass of the pulley is 3 kg. What is the acceleration of the falling mass, and what is the tension of the rope?
A horizontal rod of length L and mass M has a mass m at one end. It is supported by pivot P on the wall at the left end and a cable at angle θ\theta of at the other end as shown.
a) Find the tension in the cable.
b) If the cable snaps, with what angular velocity will the rod swing down and slam into the wall? (That is, what will the angular velocity be as it collides with the wall?)
Tension and centripetal force
The 4.00-kg block in the figure is attached to a vertical rod by means of two strings. When the system rotates about the axis of the rod, the strings are extended as shown in the diagram and the tension in the upper string is 80.0 N.
Two strings on a spinning rod - setup, approach
The 4.00-kg block in the figure is attached to a vertical rod by means of two strings. When the system rotates about the axis of the rod, the strings are extended as shown in the diagram and the tension in the upper string is 80.0 N.
Set up the problem (a free-body diagram, find unknown angles and distances, define coordinates) and then go to the next activity. Ask yourself: how do we deal with the rpm quantity in part (b)?
Practice: Pulley
You set up a pulley system as shown. There is kinetic friction acting on the top block (μk=0.175\mu_k=0.175) which has mass 4.5 kg. The vertical block has mass 10.0 kg.
Method of joints example
Consider the structure below. The triangles are equilateral. Label the members with letters A through G. A and B are the top two members, from left to right; C, D, E, F are the vertical members, left to right; G is the bottom member.
a) Without doing any calculations, label each member as being either in tension or compression.
b) Determine F1 and F5 in terms of F.
Forces: Torque
A wooden beam of mass 150 kg and length 10m is suspended from a horizontal wall support at the left end and connected by a cable to the same wall at the right end. The cable makes an angle of 45º with the horizontal. A person of mass 42 kg stands on the beam 2.5 m from the left wall. A 25 kg child also rests on the beam, at 7m from the left wall. Calculate (a) the tension in the rope and (b) the magnitude of the force exerted by the wall on the beam.
(Hint for part (b): there are two components. We want the magnitude, but you still need to consider both parts to find the correct magnitude.)
A tent post of length L is held up by two wires connected to the ground. If the tension in the right wire is 30.0 N, what is the tension in the left wire?
A camper hangs a 100kg pack to two separate trees. The two pieces of rope he uses are of different lengths, so the angles of depression (below horizontal) are 30o and 60o. Find the tension in each rope.
A 700kg elevator accelerates upward at 5m/s2, pulled by a cable of negligible mass. Find the tension force in the cable.
Practice: Pulley (no friction)
A giant ice cube of mass 400 kg is on an icy surface (there is no friction). The ice cube is connected by a weightless pulley to a mass that is hanging off the side of the surface below. You do not know the mass of the second object, but you want to measure it.
You release the ice cube from rest and let it slide. It begins to move, accelerating at a constant rate, and you measure that it travels 7.2 cm in 10 seconds. What is the mass of the object?
A camper hangs 100.0kg pack between two trees using two separate ropes of different lengths. One rope hangs at 60.0o below the top of the trees, and the other hangs at 30.0o. Find the tension in each rope.
A 5 kg5\ kgblock is being pulled along at table by a cable and is accelerating along the surface at 2m/s2m/s. The coefficient of kinetic friction between the block and the table is 0.100.10. Draw the
system then find the tension in the cable. Does the force in the cable change if the system is frictionless? Why or why not?
Two masses on a pulley on a slope
Two blocks of mass m and M are connected via pulley with a configuration as shown. The surfaces are frictionless. If M=15 kg and m=8 kg and θ1=30 and θ2=60\theta_1=30\ {\rm and}\ \theta_2=60,
a) Find the acceleration of the system.
b) What is the tension in the string?
Practice: Pulley
You set up a pulley system as shown. There is kinetic friction acting on the top block (μk=0.175\mu_k=0.175) which has mass 4.5 kg. The vertical block has mass 10.0 kg.
(three significant numbers)
Let's say Bob weighs 50kg and Joe weighs 100kg and they are playing a game of tug of war, where the tension in the rope is 50N. Ignore friction to solve for the acceleration of the two men.
Two masses on a pulley
If M = 10.0kg and m = 5.0kg, find the net acceleration of the masses. Assume the pulley and strings are frictionless and of negligible mass. Enter your answer with 2 significant digits, units are m/s2.
Two blocks of mass m1=2kg,m2=4kgm_1 = 2kg, m_2 = 4 kg are connected over a pulley as shown below. The pulley has mass M = 1kg and radius R= 2 cm. What is the acceleration of the blocks and the tension in the rope on either side of the pulley? (HINT: The tension must be different or the pulley would not rotate.)
Inclined pully system
Two blocks are connected by a pulley system. One block (10 kg) rests on a plane inclined at 35º to the horizontal, while the other block (5.0 kg) hangs off the edge of the incline. The coefficient of friction between the block and the table is 0.30. The blocks are released from rest, what are their accelerations and what is the tension?
1) Two masses are attached together by a rope as shown in the picture. If the system is released from the rest, what is the direction of the motion and acceleration for each mass? (Imagine there is no friction between masses and the inclined surface) M2 = 2M1 = 2kg
A 700kg elevator accelerates upward at 5m/s2, pulled by a cable of negligible mass. Find the tension force in the cable. What happens if the elevator accelerates downward?
A camper hangs a 100-kg pack between two trees using separate ropes of different lengths, as shown in the figure. Find the tension in each of the ropes.
A round spherical steel ball is hanging from ceiling via two ropes as shown below. Ropes are identical and maximum tension they tolerate is 150 Newton. Find maximum weight of the ball that these ropes can handle without breaking.
An object with mass M is hanging from a massless ring that is supported by two identical ropes attached to vertical walls. The ropes can tolerate maximum tension of 1200 N. What is maximum value for M that is allowed without breaking the ropes?
A) 162 kg B) 136 kg C) 112 kg D) 151 kg
Let's say Bob weighs 50kg and Joe weighs 100kg and they are playing a game of tug of war, where the tension in the rope is 50N. Ignore friction to solve for the acceleration of the two men.
Forces: Tension
A 700kg elevator accelerates upward at 5m/s2, pulled by a cable of negligible mass. Find the tension force in the cable.
If M = 10kg and m = 5kg, find the net acceleration of the masses. Assume the pulley and strings are frictionless and of negligible mass.
A camper hangs 100kg pack between two trees using two separate ropes of different lengths. Find the tension in each rope.
Two blocks are connected by a light string which passes over two pulleys as shown. The string and the pulleys are massless and there is no friction. A scale located between two pulleys. The heavier block has a mass of 5kg, and the lighter block has a mess of 3kg. What is the reading on the scale (Pick the closest answer)
Force of friction
A 400-gram package lying on a horizontal surface is attached to a horizontal string that passes over a smooth pulley. When a mass of 200 grams is attached to the other end of the string, the package is on the point of moving. Find the coefficient of friction.
A block of mass 4 kg is suspended on two strings between two walls. The angles each string makes below the horizontal is 30°. What is the tension forces in each string? Provide an answer in Newtons and 1 decimal place.
Force of tension
A monkey of mass 10kg climbs up a vertical string suspended from a hook with an acceleration of 2m/s2 . Find tension in the string.
More Inclined Surfaces Questions:
Problems on Work and Energy
A 2.00-kg block is pushed against a spring with negligible mass and force constant k= 400 N/m, compressing it 0.220 m. When the block is released , it moves along a friction-less , horizontal surface and then up a friction-less incline with slope 37.0∘37.0^{\circ}(Fig).
(a) What is the speed of the block as it slides along the horizontal surface after having left the spring?
(b) How far does the block travel up the incline before starting to slide back down?
Forces: Block on slope with friction
A mass of 5 kg5\ kg is stationary on the surface of an inclined surface with angle of θ\theta and coefficient of kinetic friction of 0.30.3 and coefficient of static friction of 0.50.5. You start increasing the angle of the inclines surface.
Problems on Work and Energy
A 2.00-kg block is pushed against a spring with negligible mass and force constant k= 400 N/m, compressing it 0.220 m. When the block is released , it moves along a friction-less , horizontal surface and then up a friction-less incline with slope 37.0∘37.0^{\circ}(Fig).
(a) What is the speed of the block as it slides along the horizontal surface after having left the spring?
(b) How far does the block travel up the incline before starting to slide back down?
trapezoid and friction
Two blocks are attached by a rope over a pulley and are placed on an incline as shown below. A force F is applied to prevent the top block from moving toward the right. If the static and kinetic coefficients of friction of all surfaces are 0.15 and 0.08 respectively, what is the minimum magnitude of F required to prevent being pulled to the right? (Hint: always start these problems with a free-body diagram!)
Two blocks of mass m and M are connected via pulley with a configuration as shown. The surfaces are frictionless. If M=15 kg and m=8 kg and θ1=30 and θ2=60\theta_1=30\ {\rm and}\ \theta_2=60
Find the acceleration
What is the tension in the string?
A 1.2 kg is at rest on a spring at the base of a 35 degree inclined plane. If the spring constant is 105 N/m, and the spring is compressed by 12 cm, how far will it travel up the incline when it is release?
If the coefficient of static friction between the block and the ramp is 0.40.4, find the minimum angle such that the block will slide down the slope.
Stacked blocks on a pulley and slope
Block A with mass 5 kg is connected to block B with mass 10 kg via a pulley. They are initially at rest on a 30-degree slope. Write out the equations from Newton's laws and find the distance they have moved in 4s. Neglect friction.
Stacked blocks on a pulley and slope
Block A with mass 5 kg is connected to block B with mass 10 kg via a pulley. They are initially at rest on a 30-degree slope. Write out the equations from Newton's laws and find the distance they have moved in 4s. Neglect friction.
Stacked blocks on a pulley and slope
Block A with mass 5 kg is connected to block B with mass 10 kg via a pulley. They are initially at rest on a 30-degree slope. Write out the equations from Newton's laws and find the distance they have moved in 4s. Neglect friction.
Stacked blocks on a pulley and slope
Practice: Stacked Blocks on Pulley with Slope
Block A with mass 5 kg is connected to block B with mass 10 kg via a pulley. They are initially at rest on a 30-degree slope. Write out the equations from Newton's laws and find the distance they have moved in 4s. Neglect friction.
Problems on Work and Energy
Practice: Block with Spring and Ramp
A 2.00-kg block is pushed against a spring with negligible mass and force constant k= 400 N/m, compressing it 0.220 m. When the block is released , it moves along a friction-less , horizontal surface and then up a friction-less incline with slope 37.0∘37.0^{\circ}(Fig).
(a) What is the speed of the block as it slides along the horizontal surface after having left the spring?
Forces: Block on slope with friction
A mass of 5 kg5\ kg is stationary on the surface of an inclined surface with angle of θ\thetaand coefficient of kinetic friction of 0.30.3 and coefficient of static friction of 0.50.5. You start increasing the angle of the inclines surface.
Two masses on a pulley on a slope
Two blocks of mass m and M are connected via pulley with a configuration as shown. The surfaces are frictionless. If M=15 kg and m=8 kg and θ1=30 and θ2=60\theta_1=30\ {\rm and}\ \theta_2=60,
Find the acceleration of the system.
What is the tension in the string?
Minimum sliding angle
If the coefficient of static friction between the block and the ramp is 0.40.4, find the minimum angle such that the block will slide down the slope. Give your answer to two sig figs in degrees.
I over-packed a box and it weighs 50kg. I'm pulling it across a rough surface at an angle of 45 degrees above the horizontal with a force of 280N. The coefficient of kinetic friction of the floor is 0.50. I pull for 10 seconds, which causes the box speed up from rest. Then I release it, and it continues to slide, as it slows to a halt.
a) What is its maximum speed?
b) How long until it stops?
Stacked blocks on a pulley and slope
Block A with mass 5 kg is connected to block B with mass 10 kg via a pulley. They are initially at rest on a 30-degree slope. Write out the equations from Newton's laws and find the distance they have moved in 4s. Neglect friction.
Inclined pully system
Two blocks are connected by a pulley system. One block (10 kg) rests on a plane inclined at 35º to the horizontal, while the other block (9.0 kg) hangs off the edge of the incline. The coefficient of friction between the block and the table is 0.30. The blocks are released from rest, what are their accelerations and what is the tension?
Practice: Springs and slopes
A 2.00-kg block is pushed against a spring with negligible mass and force constant k= 400 N/m, compressing it 0.220 m. When the block is released , it moves along a friction-less , horizontal surface and then up a friction-less incline with slope 37.0∘37.0^{\circ}(Fig).
Component vectors practice 2
A block of weight 30 N is sitting on an incline of 19 degrees.
a) What are the components of the block's weight in the directions parallel to, and perpendicular to, the slope?
b) What is the mass of this block?
Forces: Inclined surfaces
Consider a segment of a light rail train banked at 4.0 degrees from horizontal spanning a turn with a radius of curvature of 450 meters. Neglect friction. What speed was this light rail designed for? (in m/s, rounded to 1 decimal place)
This question is adapted from Chapter 6, problem #75 in the Openstax Physics textbook, which is free and open-source: https://openstax.org/details/books/university-physics-volume-1
Slide and collide
A 5.00kg box is sliding down a 20.0m tall slide that makes an angle of 60.0o with the ground. The coefficient of friction for the slide is 0.750.
At the bottom of the slide it slides on a frictionless surface and collides with a 2.50kg stationary mass.
If the coefficient of static friction between the 2.00kg block and the ramp is 0.4000.400, find the minimum angle such that the block will slide down the slope (in degrees).
Problems on Work and Energy
A 2.00-kg block is pushed against a spring with negligible mass and force constant k= 400 N/m, compressing it 0.220 m. When the block is released , it moves along a friction-less , horizontal surface and then up a friction-less incline with slope 37.0∘37.0^{\circ}(Fig).
(a) What is the speed of the block as it slides along the horizontal surface after having left the spring?
(b) How far does the block travel up the incline before starting to slide back down?
Work on wagon
A 20kg wagon rests on an inclined plane with angle 30°. The wagon is pulled by a 200N tension force along the plane and is displaced by 2 m. The coefficient of kinetic friction between the surfaces is 0.30.
a) Draw a free-body diagram for the wagon.
b) Find the work done by each force on the wagon.
Block on Slope with Friction
A mass of 5.0 kg5.0\ kg is stationary on the surface of an inclined surface with angle of θ\thetaand coefficient of kinetic friction of 0.300.30 and coefficient of static friction of 0.500.50. You start increasing the angle of the inclines surface.
a) At what angle does the mass start to slide down? (Round to the nearest whole number)
b) If you set the system at an angle which is 5 degrees more than the angle you found in part a), how much time does it take for the speed of the mass to reach 2.0 m/s2.0\ m/s? (Units are in seconds, write the answer so that it has one digit)
A block with mass m is set to move up an inclined plane.
a) Assume there is no friction, how far will the block slide before come to a stop?
b) Now, assume there is friction between the block and the plane, how far will the block go up the plane?
1) Two masses are attached together by a rope as shown in the picture. If the system is released from the rest, what is the direction of the motion and acceleration for each mass? (Imagine there is no friction between masses and the inclined surface) M2 = 2M1 = 2kg
Practice: Inclined Plane Theory
Inclined Plane
Sliding down an inclined plane is another example of motion with constant acceleration.
Source of the motion is still gravity of earth but only part of it is affecting the sliding of the object
trapezoid and friction
Two blocks are attached by a rope over a pulley and are placed on an incline as shown below. A force F is applied to prevent the top block from moving toward the right. If the static and kinetic coefficients of friction of all surfaces are 0.15 and 0.08 respectively, what is the minimum magnitude of F required to prevent being pulled to the right? (Hint: always start these problems with a free-body diagram!)
Practice: Inclined Plane
A box of 10 Kg10\ Kg is released from rest at t=0 st=0\ sfrom the top of a frictionless inclined surface with θ=45°\theta=45\degree. If the box is initially at the top of inclined surface with height of 2 m2\ mrespect to the bottom of the ramp, at what time the box gets to the ground?
Practice: Friction
A 10-kg box is initially at rest on flat surface. A horizontal force of 28 Newton is applied on it. The static and kinetic coefficient of friction between the box and the floor is 0.32 and 0.18. What is the magnitude of the friction force?
Work Done by Multiple Forces
A 20 kg wagon rests on an inclined plane with angle 30°. The wagon is pulled by a 200 N tension force along the plane and is displaced by 2 m. The coefficient of kinetic friction between the surfaces is 0.3.
a) draw all the forces.
b) Find the work done by each force on the box.
Two different boxes of masses m1 = 125kg and m2 = 45kg are sliding down a rough inclined plane angled at θ=35∘\theta = 35^\circ , as seen in the figure. The coefficient of kinetic friction between m1 and the plane is 0.3. The coefficient between m2 and the plane is 0.5. Find the acceleration of the two boxes and the contact force between them.
A 1400-kg truck ascends a steep road at a speedy 60 km/h, against a 450-N force of air resistance. If the engine supplies energy to the drive wheels at the rate of 38 kW, what is the slope of the road?
A fixed triangular wedge has two inclined surfaces forming a double inclines plane. Two masses m1 = 5 kg and m2 = 10 kg are attached to a massless pulley connected with an inextensible string. The inclined surface I1 and I2 make an angle α1=60∘\alpha_1=60^\circ and α2=30∘\alpha_2=30^\circ with the horizontal respectively. The coefficient of kinetic friction is μ=0.01.\mu=0.01. Assume g = 10 m/s2.
a) Draw a free body diagram.
b) Is the system stationary? If not what will be the net acceleration?
A 1.2 kg is at rest on a spring at the base of a 35 degree inclined plane. If the spring constant is 105 N/m, and the spring is compressed by 12 cm, how far will it travel up the incline when it is release?
A stationary snow/water skier starts to slid down an icy slope inclined 11° until it hits the water. Initially skier is 200 meter away from the surface on the inclined surface. When he hits the water, the skier comes to full stop in 80 meters on the surface of water.
a) What is the acceleration of the skier on the icy slope?
b) How long does it take for the skier to hit the water?
A car travelling at 25 m/s on an uphill with θ = 20° slope runs out of the gas. a) How far up the hill it can move before starting to roll back down?
b) How long does it take for the car to get to the turning point?
a) Dave is trying to push a 60kg box up a greased ramp inclined 30°, pushing with a force of 350N. He pushes the box perfectly horizontally, rather than up the ramp, because he’s not terribly bright. What is the box’s acceleration?
b) If Dave forgot his grease at home, the ramp would have μsmax=0.10\mu_{\rm smax}=0.10 and μk=0.05.\mu_k=0.05. He still insists on pushing the box horizontally, with the same force. What would the box’s acceleration be now?
I'm moving and packed all my books into a box that weighs 17kg. I pull the box on a weightless dolly with a force of 60N at an angle of 30° to the horizontal surface. What is the acceleration of the box?
If the coefficient of static friction between the block and the ramp is 0.40.4, find the minimum angle such that the block will slide down the slope.
Forces: Inclined surface
A 40kg wagon attached to a rope is pulled up a hill at an incline of 19° to the horizontal. If the wagon starts from rest and takes 50 seconds to move 92 m up the hill, what is the force of tension in the rope? Find the acceleration of the block.