Object moving in the opposite direction of a single force

[henry3369]

A hammer is hanging by a light rope from the ceiling of a bus. The ceiling of the bus is parallel to the roadway. The bus is traveling in a straight line on a horizontal street. You observe that the hammer hangs at rest with respect to the bus when the angle between the rope and the ceiling of the bus is 67 degrees. What is the acceleration of the bus?

Well I know how to solve this, but I'm confused as to why the ball moves in the opposite direction of the force. Say for example the bus moves right, then the ball goes back slightly. When I break the force into components there is one component pointing upwards and one component to the right. But if there is only 1 force acting on the ball and it is to the right, why is the ball going to the left?

 

[A.T.]

But if there is only 1 force acting on the ball and it is to the right, why is the ball going to the left?

The frame of the bus is non-inertial, so there is an inertial force to the left.
http://en.wikipedia.org/wiki/Fictitious_force

 

[Doc Al]

Well I know how to solve this, but I'm confused as to why the ball moves in the opposite direction of the force. Say for example the bus moves right, then the ball goes back slightly. When I break the force into components there is one component pointing upwards and one component to the right. But if there is only 1 force acting on the ball and it is to the right, why is the ball going to the left?

Realize that the bus and thus the hammer (ball?) are accelerating. There are two forces acting on the object: gravity and the tension in the rope. If the bus accelerates to the right, then the net force on the object will be to the right. In order for the rope to drag the object along with the bus, it must make an angle with the vertical that is opposite to the direction of the acceleration. The ball accelerates to the right, but hangs to the left of vertical.

You can also view this in terms of inertial forces when viewed from the non-inertial frame of the bus, as A.T. said.

 

[CWatters]

But if there is only 1 force acting on the ball and it is to the right, why is the ball going to the left?

The ball is trying to go straight. It just looks like it's going left because the bus is going right.

 

[BvU]

But if there is only 1 force acting on the ball and it is to the right, why is the ball going to the left

There are two forces working on the ball. And the ball isn't going to the left.

The two forces are gravity and the tension from the wire. The (vector) sum of the two forces determines the motion of the ball.

If the bus stands still, the wire is vertical and the tension and the gravity forces are equal and opposite, so the net force on the ball is zero: it hangs still.

If the bus moves with constant velocity (and we wait long enough for a possible swinging to dampen out), again the wire is vertical and the tension and the gravity forces are equal and opposite, so the net force on the ball is zero: it moves with constant velocity.

If the bus accelerates with constant acceleration (and we wait long enough for a possible swinging to dampen out), the ball hangs still for a passenger in the bus. For an observer standing still on the road, the ball accelerates with the same acceleration as the bus. Since the gravity is still pulling straight down, the only force that can bring this acceleration about is the tension in the string. So it has to pull forward while at the same time pulling up to offset the force from gravity.
The wire can only pull in a direction along the wire (try it with a piece of string -- I'm not joking, it's an important insight!) so it hangs as you describe. So the tension forcr from the wire on the ball has an upward component (mg) and a forward component (ma).

If the bus brakes (again with constant deceleration = acceleration in a direction opposite the motion) same story but pulling is now backwards to decelerate the ball.

Try it all out on your next ride with train, car or bicycle with a makeshift pendulum. How it hangs in a left turn, a right turn, etc.

And if you really want to wonder, same thing with a helium ballloon on a string. Won't work for the bicycle case because of the wind spoiling the simplicity.