1. What is the work W m done by the student? W m = 2. At the top of the incline,

Question

1. What is the work Wm done by the student? Wm =

2. At the top of the incline, the string by which she was pulling the block breaks. The block, which was at rest, slides down a distance d = 4.5 m before it reaches a frictionless horizontal surface. A spring is mounted horizontally on the frictionless surface with one end attached to a wall. The block hits the spring, compresses it a distance L = 0.6 m, then rebounds back from the spring, retraces its path along the horizontal surface, and climbs up the incline.What is the speed v of the block when it first reaches the horizontal surface? v =

3.What is the spring constant k of the spring?k =

4. How far up the incline d1 does the block rebound?d1 =

A physics student pulls a block of mass m = 20 kg up an incline at a slow constant velocity for a distance of d = 4.5m. The incline makes an angle = 30° with the horizontal. The coefficient of kinetic friction between the block and the inclined plane is k = 0.2.

Explanation / Answer

(1)
Work done by student, = Work done against Gravitational Potential Energy + Work done against friction.
Wm = m*g*d*sin(30) + uk*m*g*cos(30)*d
Wm = 20*9.8*4.5*sin(30) + 0.2*20 * 9.8*cos(30) * 4.5
Wm = 593.8 J

(2)
Let the Speed of the block when it first reaches horizontal surface = v
Now Initial Potential Energy = Final Kinetic Energy + Energy wasted in Friction
m*g*d*sin(30) - uk*m*g*cos(30)*d = 1/2*mv^2
20*9.8*4.5*sin(30) - 0.2*20 * 9.8*cos(30) * 4.5 = 1/2*20*v^2
v = 5.37 m/s

(3)
Let the spring constant be k,

Now Using Energy conservation,
Kinetic Energy = Sprng potential Energy
1/2*mv^2 = 1/2*kx^2
20*5.37^2 = k*0.6^2
k = 1602.1 N/m

(4)
Initial Kinetic Energy = Final Potential Energy + Energy wasted in Friction
1/2*m*v^2 = m*g*d1*sin(30) + uk*m*g*cos(30)*d1
1/2*20*5.37^2 = 20*9.8*d1*sin(30) + 0.2*20*9.8*cos(30)*d1
d1 = 2.19 m

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