# Physics

posted by .

A 20lb ball is 1 ft. in diameter and has a angular velocity of 300 rpm when it is 2 ft. away from the plate. The coefficient of rolling friction between the surface and the ball is μs = 0.3. It strikes the 1-ft. high, 10-lb plate that is held in place by an unstretched spring of stiffness k = 400 lb/ft. Take e = 0.8 between the ball and the plate and assume that the plate slides smoothly.

Find the maximum compression imparted to the spring.

• Physics -

I used to work with SI units:
m1 = 20 lb = 9.07 kg,
m2 = 10 lb = 4.536 kg,
R = 1ft = 0.305 m,
s =2 ft = 0.61 m.
k =400 lb/ft = 5837 N/m,
μ = 0.3,
coefficient of restitution e = 0.8.
For the ball:
n1 = 300 rpm = 5 rev/s =>
ω1 =2• π•n(b1) = 10•π =>
v1 = ω(b1) •R = 10•π•0.305 =9.58 m/s.

The kinetic energy of the rolling ball at its initial position is
KE1 =m•v1^2/2 +I •ω1^2/2 = m•v1^2/2 +(2•m•R^2/5) • (v1^2/2•r^2) = 0.7•m1•v1^2 =0.7•9.07•(9.58)^2 = 583 J.
KE1 – KE2 =W(friction)
W(friction) = μ•m•g•s =0.3 •9.07•9.8•0.61 = 16.27 J.
KE2 = KE1 - W(friction) = 583 - 16.27 = 566.73 J.
KE2 =m1•v2^2/2,
v2 = sqrt(2•KE2/m1) = sqrt(2•566.73/9.07) = 11.18 m/s.
Law of conservation of linear momentum:
m1•v2 = m1•v3 +m2•u
According to the definition the coefficient of restitution is
e = (u – v3)/v2,
e•v2 = u – v3
v3 = u - e•v2.
m1•v2 =m1• (u - e•v2) + m2•u = m1• u - m1• e•v2 + m2•u.
u• (m1+m2) = m1•v2• (e + 1 )
u = m1•v2(e + 1 )/ (m1+m2) =
9.07•11.18•1.8/(9.07 + 4.536) = 13.42 m/s.
k•x^2/2 = m2•u^2/2,
x =u•sqrt(m2/k) = 13.42•sqrt(4.536/5837) = 0.37 cm ≈ 1.2 ft.
Maybe I’ve mistaken in calculations (especially due to the units transformation), but the general form is correct. If you know the answer, post it

## Similar Questions

1. ### ap phyiscs

A bowler throws a bowling ball of radius R=11 cm down a lane. The ball slides on the lane, with initial speed v(of the center of mass)=7 m/s and initial angular speed =0. The coefficient of kinetic friction between the ball and the …
2. ### Physics

A uniform, spherical bowling ball of mass m and radius R is projected horizontally along the ﬂoor at an initial velocity v0 = 6.00 m/s. The ball is not rotating initially, so ω0 = 0. It picks up rotation due to (kinetic) …
3. ### physics

A 32 g ball rolls around a 40 cm diameter L-shaped track, shown in the figure below, at 60 rpm. Rolling friction can be neglected. What is the magnitude of the net force exerted on the ball?
4. ### physics college

A billiard ball that is initially at rest is given a sharp blow by a cue stick. The force is horizontal and is applied at a distance h = 2R/3 below the centerline, The speed of the ball just after the blow is v0 and the coefficient …
5. ### Physics

A ball and a thin plate are made from different materials and have the same initial temperature. The ball does not fit through a hole in the plate, because the diameter of the ball is slightly larger than the diameter of the hole. …
6. ### Physics

Thanks for taking a look! A baseball of mass m1 = 0.46 kg is thrown at a concrete block m2 = 8.25 kg. The block has a coefficient of static friction of μs = 0.81 between it and the floor. The ball is in contact with the block …
7. ### I need help with Physics

A baseball of mass m1 = 0.46 kg is thrown at a concrete block m2 = 8.25 kg. The block has a coefficient of static friction of μs = 0.81 between it and the floor. The ball is in contact with the block for t = 0.165 s while it collides …
8. ### physics

A baseball of mass m1 = 0.32 kg is thrown at a concrete block m2 = 6.25 kg. The block has a coefficient of static friction of μs = 0.71 between it and the floor. The ball is in contact with the block for t = 0.195 s while it collides …
9. ### Physics

A spherical bowling ball with mass m = 3.2 kg and radius R = 0.107 m is thrown down the lane with an initial speed of v = 8.6 m/s. The coefficient of kinetic friction between the sliding ball and the ground is μ = 0.34. Once the …
10. ### Physics

A student drops a lead ball 4" in diameter from the top of a large live oak tree. As the ball is falling, a bird flies under it, slowing the ball's velocity to 30 feet/sec. Two seconds later the ball strikes the ground. What is the …

More Similar Questions