# physics

posted by .

A thin uniform stick having a mass of 0.680 kg and a length of 1.50 m is at rest, hanging vertically from a strong, fixed hinge at the uppermost end of the stick. The stick is free to swing back and forth in an Up-Down-East-West plane. Suddenly, the midpoint of the stick is struck by a hammer; the force on the stick by the hammer is 12.7 N towards the East.

(a) Find the magnitude of the resulting acceleration of the center of mass of the stick.

(b) While the 12.7-N force is being applied, find the horizontal force on the stick by the hinge.

(c) There is some point at which the hammer can strike the stick such that the horizontal force on the stick by the hinge will be zero, even though the stick is being struck by the hammer at that instant. Calculate the distance from the hinge to the location of this special point.
At__________m below the hinge.

• physics -

M=Torque about hinge = 12.7 * .75 = 9.525
I about hinge = (1/3) m l^2 = (.68/3)2.25
= .51

angular acceleration alpha = M/I = 9.525/.51 = 18.7 radians/s^2

resulting linear acceleration of center East = .75 alpha = 14 m/s^2 (part a)

we better get the same acceleration East from the sum of forces on the stick
12.7east + force from hinge F = .68 (14)

12.7 + F = 9.52
F = -3.18 or 3.18 N west

Now the sweet point:
Torque
M = 12.7 x
alpha = 12.7 x/.51 = 24.9 x
a of center = .75 alpha = 18.7 x meters/s^2

F = m a
18.7 x = F/m but F is just 12.7 because the hinge force is zero so
18.7 x = 12.7/.68
x = 1 meter, the end of the stick

Try this with a mass distribution like a baseball bat or tennis racquet and the result will make more sense :)

• physics -

thanks

• physics -

Oh, one meter is not the end of the stick. It is 2/3 of the way out.

• physics -

Which is about how far out on a bat you want to hit the ball without stinging your hand.

## Similar Questions

1. ### physics

A uniform 2.00-m-long stick is raised at an angle of 30° to the horizontal above a sheet of ice. The bottom end of the stick rests on the ice. The stick is released from rest. The bottom end of the stick remains in contact with the …
2. ### physics

A meter stick is held vertically with one end on the floor and is then allowed to fall. Find the speed of the other end when it hits the floor, assuming that the end on the floor does not slip. (Hint: Consider the stick to be a thin …
3. ### physics

One end of a meter stick is pinned to a table, so the stick can rotate freely in a plane parallel to the tabletop. Two forces, both parallel to the tabletop, are applied to the stick in such a way that the net torque is zero. The first …
4. ### College Physics

A uniform meter stick of mass M has an empty paint can of mass m hanging from one end. The meter stick and the can balance at a point 19.9 cm from the end of the stick where the can is attached. When the balanced stick-can system is …
5. ### physics

One end of a meter stick is pinned to a table, so the stick can rotate freely in a plane parallel to the tabletop. Two forces, both parallel to the tabletop, are applied to the stick in such a way that the net torque is zero. The first …
6. ### phyics

One end of a meter stick is pinned to a table, so the stick can rotate freely in a plane parallel to the tabletop. Two forces, both parallel to the tabletop, are applied to the stick in such a way that the net torque is zero. The first …
7. ### PHYICS

One end of a meter stick is pinned to a table, so the stick can rotate freely in a plane parallel to the tabletop. Two forces, both parallel to the tabletop, are applied to the stick in such a way that the net torque is zero. The first …
8. ### physics

a uniform (in density and shape) stick is balanced by one end on the ground and the other tied to a massless horizontal rope attached to a wall as shown in the figure. The stick's mass is 10kg and its length is 5m. a. Calculate the …
9. ### Physics

A thin stick of mass M = 3.1 kg and length L = 1.6 m is hinged at the top. A piece of clay, mass m = 0.7 kg and velocity V = 4.0 m/s hits the stick a distance x = 1.20 m from the hinge and sticks to it. 1. What is the angular velocity …
10. ### Physics

A meter-long stick is balanced vertically on the ground. It is then made to fall with a gentle nudge. What is the speed of the end of the stick as it hits the floor?

More Similar Questions