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Slide and collide

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Wize University Physics Textbook (Master) > Momentum, Impulse and Collisions

Collisions

7 Activities

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

Inclined Surfaces

3 Activities

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.




What is the speed of the 5.00 kg mass at the bottom of the slide? (answer in m/s)
More Collisions Questions:
Problem Set-Momentum
Practice: 2D Linear Momentum Conservation
You throw a 5 kg ball directly eastward at 6 m/s toward a stationary 4 kg ball.  After colliding, the 5 kg ball is deflected 45° north of the horizontal at a speed of 2 m/s.  What is the speed and direction of the 4 kg ball after collision? Is this collision elastic?
Perfectly inelastic car crash
Practice: 2D Inelastic Collision
Two cars collide at an intersection. Car A, with a mass of 2000.0 Kg, is going from west to east, while car B, of mass 1500 kg, is going from north to south at 15 m/s. As a result of this collision, the two cars become mushed and move as one afterward. In your role as an expert witness, you inspect the scene and determine that, after the collision,the enmeshed cars moved at an angle of 65∘ 65^{\circ}\ south of east from the point of impact.
(a) How fast were the enmeshed cars moving just after the collision?
Practice: 1D Collision
A ball of mass 0.500kg moving at 4.00m/s hits a stationary ball of mass 3.50kg. Assume no friction in this system and the collision is elastic, what are the final velocities of the two balls?
Kinematics: Momentum
One pool ball of mass 14.0 grams traveling with a velocity of 5 m/s (Ball A) hits another ball of mass 23.0 grams moving at 3.4 m/s (Ball B). The collision is head-on and elastic. Find the final speeds of both balls after the collision.
Practice: Car crash (inelastic)
Two cars collide at an intersection. Car A, with a mass of 2000 Kg, is going from west to east, while car B, of mass 1500 kg, is going from north to south at 15 m/s. As a result of this collision, the two cars become enmeshed and move as one afterward.In your role as an expert witness, you inspect the scene and determine that, after the collision,the enmeshed cars moved at an angle of 65∘ 65^{\circ}\ south of east from the point of impact.
Momentum and spring
A 15.0-kg block is attached to a very light horizontal spring with spring constant 500 N/m and is resting on a friction-less horizontal table. It is struck by a 3.00-kg stone traveling horizontally at 8.00 m/s to the right. The stone rebounds at 2.00 m/s horizontally to the left. Find the maximum distance that the block will compress the spring after the collision.
Momentum: Colliding balls
You throw a 5 kg ball directly eastward at 6 m/s toward a stationary 4 kg ball.  After colliding, the 5 kg ball is deflected 40° north of the horizontal at a speed of 2 m/s.
Kinematics and Simple Harmonic Motion
A 12 g bullet moving horizontally at 30 m/s is fired into a hanging mass of 2.5 kg. The bullet becomes embedded in the hanging mass, which then acts like a pendulum. The cord connecting the mass to the ceiling is 75.0 centimeters.
Kinematics: Momentum
A bowling ball (mass 5.0kg) travelling at 0.75 m/s hits a bowling pin (mass 1.6kg), initially at rest. The bowling pin moves off with a speed of 1.25 m/s at an angle of 35º relative to the initial direction of the bowling ball. What is the final velocity of the bowling ball?
(Important hint: You cannot assume the collision is elastic.).
Select a magnitude and a direction from the options below.
Kinematics: Momentum
Particle m1 with mass of4×10−25 kg4\times 10^{-25}~\rm kgis travelling with a velocity of 5msı^5\frac{m}s\hat\imath , and collides with particle m2 with mass 6×10−25 kg6\times 10^{-25}~\rm kg which is initially at rest. After the interaction, m1 travels with a speed of 5 m/s, deflected by an angle of 45 degrees relative to its initial path.
a) What is the total momentum of the system?
b) What is the velocity of m2 after the collision?
Conservation of Momentum
A car accidentally enters a playground at a velocity of 14m/s. A child tosses a ball at the car at 18m/s. What is the ball's speed after it rebounds elastically from the car? (Assume it's a head-on collision.)
Momentum: Swinging ball hits another ball
A ball of mass 0.50 kg is attached to a string of length 26 cm. The ball is raised so that the string is taut and horizontal. Now the ball is released such that it swings and undergoes an elastic head-on collision with a stationary ball of mass 0.20kg that is free to roll horizontally. The mass strikes the ball when the string is vertical (that is, it falls through a full 90 degrees before hitting the ball).
Kinematics: Radioactive decay and momentum
A radioactive atom at rest with a mass of 100×10−27 kg100\times 10^{-27}~kgundergoes decay to three particles with masses of 25×10−27 kg25\times 10^{-27}~kg , 40×10−27 kg40\times 10^{-27}~kg and 35×10−27 kg35\times 10^{-27}~kg respectively. Assume that all three particles remain in the x-y plane.
If the first particle is moving in the direction of positive y axis at speed of 20m/s and the second particle moves in the direction of 25 degree clockwise respect to positive x-axis at speed of 15 m/s, what is the angle and speed of the of the third particle?
(Note: if you are wondering why the masses don't add up, it's because of special relativity and mass-energy equivalence. Something to Google if you're interested. If these were anything other than atomic nuclei, though, you should expect the masses to add up properly.)
Collision practice
A 4.0 kg ball with a velocity of 3.0 m/s at 45º to the horizontal collides in an elastic collision with a 3.5 kg ball initially at rest. The 4.0kg ball moves off at 2.0 m/s at 30º to the horizontal. What is the final velocity of the 3.5 kg ball?
Dropping a big and small ball
Two balls are dropped from rest, with one directly above the other. The lower ball has a mass 10 times that of the higher ball. Assume that all collisions between the balls and with the floor are elastic. How high will each ball rebound, compared to the initial drop height h?
Practice: BMW and truck collision
A 1200-kg BMW and a 2200-kg truck collide at a right angle in an airport crossing. They skid together for 22m; the coefficient of friction is 0.91. Show that at least one car must have exceeded the 25 km/h speed limit at the intersection.
A 5 kg chunk of ice is sliding at 12.0 m/s on the floor of an ice-covered valley when it collides with and stick to another 5.00-kg chunk of ice that is initially at rest. Since the valley is icy, there is no friction. After the collision, how high above the valley floor will the combined chunks go?
Match the terms.
A ball of mass 0.500kg moving at 4.00m/s hits a stationary ball of mass 3.50kg. Assume no friction in this system, what are the final velocities of the two balls?
Problem Set-Momentum
You throw a 5 kg ball directly eastward at 6 m/s toward a stationary 4 kg ball.  After colliding, the 5 kg ball is deflected 45° north of the horizontal at a speed of 2 m/s.  What is the speed and direction of the 4 kg ball after collision? Is this collision elastic?
Perfectly inelastic car crash
Two cars collide at an intersection. Car A, with a mass of 2000.0 Kg, is going from west to east, while car B, of mass 1500 kg, is going from north to south at 15 m/s. As a result of this collision, the two cars become mushed and move as one afterward. In your role as an expert witness, you inspect the scene and determine that, after the collision,the enmeshed cars moved at an angle of 65∘ 65^{\circ}\ south of east from the point of impact.
(a) How fast were the enmeshed cars moving just after the collision?
(b) How fast was car A going just before the collision?
Particle m1 with mass of 4kg is travelling with a velocity of 5msı^5\frac{m}s\hat\imath , and collides with particle m2 with mass 6×10−25 kg6\times 10^{-25}~\rm kg which is initially at rest. After the interaction, m1 travels with speed of 5 m/s at an angle of 45 degrees with vector.
What is the total momentum of the system?
What is the vector velocity of m2?
Momentum: Collision
Two carts on a friction less surface collide and stick to each other. What is the velocity of the two carts after collision?
A 1200-kg BMW and a 2200-kg truck collide at right angles in an airport crossing. They skid together for 22m; the coefficient of friction is 0.91. Show that at least one car must have exceeded the 25 km/h speed limit at the intersection.
Conservation of Momentum
One pool ball of mass 1 kg traveling with a velocity of 5 m/s hits another ball of mass 2 kg moving towards it at 4 m/s. The collision is head on and elastic. Find the final velocities of both balls after the collision.
Conservation of Energy & Momentum
A 12-g rifle bullet is fired with a speed of 380 m/s into a ballistic pendulum with mass 6.00 kg, suspended from a cord 70.0 cm long. Compute (a) the vertical height through which the pendulum rises , (b) the initial kinetic energy of the bullet, and (c) the kinetic energy of the bullet and pendulum immediately after the bullet becomes embedded in the pendulum.
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
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
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?
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.