Question

In: Physics

A block slides down a frictionless inclined ramp. If the ramp angle is 26° and its...

A block slides down a frictionless inclined ramp. If the ramp angle is 26° and its length is 29 m, find the speed of the block as it reaches the bottom of the ramp, assuming it started sliding from rest at the top.

Expert Solution

There are two forces acting on the block: mg is the gravitational force of the Earth, N is the normal force of the ramp on the incline. The free body diagram of the block is shown below:

The gravitational force is resolved into components parallel and perpendicular to the ramp. The block is not allowed to move in the direction perpendicular to the ramp, the net force on the block in this direction is zero.

The net force along the ramp accelerates the block, the acceleration is given by Newton's second law of motion.

Substituting we get

The acceleration of the block along the incline is constant, the motion of the block along the incline is governed by the kinematics equations for uniformly accelerated motion. To find the final speed of the block we use

where u is the initial velocity, L is the length of the ramp.

Given the block starts from rest u=0, substituting L=29m, a=4.296m/s² we get

genius_generous answered 5 months ago

A box of physics books slides down a ramp inclined at an angle of 40 degrees...

A box of physics books slides down a ramp inclined at an angle of 40 degrees to the horizontal. The total length of the ramp is 10m. The coefficient of kinetic friction between the box and the ramp is .2 for the top 8m and zero for the bottom 2m. Upon reaching the bottom of the ramp, a spring bounces the box back upward. (a) Find the distance that the box travels back up the ramp on the return bounce....

A block of mass m = 2.1 kg slides down a 36 ° inclined ramp that...

A block of mass m = 2.1 kg slides down a 36 ° inclined ramp that has a height h = 3.1 m. At the bottom, it hits a block of mass M = 7.1 kg that is at rest on a horizontal surface. Assume a smooth transition at the bottom of the ramp. If the collision is elastic and friction can be ignored, determine the distance the mass m will travel up the ramp after the collision.

A block with mass m = 17.2 kg slides down an inclined plane of slope angle...

A block with mass m = 17.2 kg slides down an inclined plane of slope angle 13.8o with a constant velocity. It is then projected up the same plane with an initial speed 4.05 m/s. How far up the incline will the block move before coming to rest?

a block slides down a frictionless inclined plane of height h=1m, making theta with the horizontal....

a block slides down a frictionless inclined plane of height h=1m, making theta with the horizontal. At the bottom of the plane, the block continues to move on a flat surface with a coefficient of friction u = 0.30. How far does the mass move on the flat surface?

A mass m slides down a frictionless ramp and approaches a frictionless loop with radius R....

A mass m slides down a frictionless ramp and approaches a frictionless loop with radius R. There is a section of the track (between the ramp and the loop) with length 2R that has a kinetic friction coefficient of 0.5. From what height h must the mass be released to stay on the track? No figure. 1.5R 2.5R 3.5R 4.5R or 5.5R

A block of mass m1 = 3.27 kg on a frictionless plane inclined at angle ?...

A block of mass m1 = 3.27 kg on a frictionless plane inclined at angle ? = 31.2

A 50 kg crate slides down a ramp that is inclined by 30 degrees from the...

A 50 kg crate slides down a ramp that is inclined by 30 degrees from the horizontal. The acceleration of the crate parallel to the surface of the ramp is 2.0m/s^2, and the length of the ramp is 10m. Determine the kinetic energy accumulated by the crate when it reaches the bottom of the ramp if it started from rest at the top of the incline. Calculate the amount of energy lost by the crate due to friction in its...

A box (with a penguin inside) with mass, M, slides down a frictionless ramp, starting a...

A box (with a penguin inside) with mass, M, slides down a frictionless ramp, starting a height H above ground level. At the lowest point of the ramp (height = -0.1H) it slides through a curved section of track with radius, R= 0.25H. The box (w/ penguin) then rises to ground level (height = 0) and at that point, leaves a jump at an angle θ. At the highest point of its trajectory, h2, it strikes a blob of glue...

A cart of mass m1 = 11 kg slides down a frictionless ramp and is made...

A cart of mass m1 = 11 kg slides down a frictionless ramp and is made to collide with a second cart of mass m2 = 24 kg which then heads into a vertical loop of radius 0.25 m (a) Determine the height h at which cart #1 would need to start from to make sure that cart #2 completes the loop without leaving the track. Assume an elastic collision. (b) Find the height needed if instead the more massive...

If a block slides down an inclined plane having friction with a spring attached to the...

If a block slides down an inclined plane having friction with a spring attached to the horizontal plane at the bottom of the plane.Find the coefficine tof kinetic friction. mass of the block is 10 kg and the angle is 30 degrees the spring constant is 500 N/m