Finding acceleration of truck from a hung mass on the ceiling of it.

[JLPG]

Homework Statement

A mass M = 74.0 kg is suspended by a massless string from the ceiling of a van which is moving with constant acceleration a, as shown in the figure.

If the string makes an angle theta = 22° with respect to the vertical, what is the acceleration a of the van?

Homework Equations

All I can think of is F=ma

The Attempt at a Solution

I found the force of the x component and the y component (-27.72N and 793.8N resp.) I tried 27.72=74.0a=.375m/s^2 and 793.8=74a=10.727m/s^2. I tried adding/substracting tthe answers. I don't know what to try anymore.

 

[cheahchungyin]

tan^-1(a/g)=22°

Look it like a triangle. the angle is 22 theta, the vertical component is g, the horizontal is a.

 

[JLPG]

Thank-you so much!

 

[cheahchungyin]

No-Problem! XD

 

[Nickie]

To find the acceleration of the truck, we can use the equation F=ma, where F is the net force acting on the truck and m is its mass. In this case, the net force is the force of gravity acting on the suspended mass, which can be broken down into its x and y components.

The x component of the force is equal to the tension in the string, which can be calculated using the angle theta and the weight of the suspended mass. The y component of the force is equal to the weight of the suspended mass.

Using these values, we can set up the following equations:

F_x = T = Mgcos(theta)
F_y = Mg = 74.0kg * 9.8m/s^2 = 725.2N

Since the truck is moving with constant acceleration, the net force acting on it must also be constant. Therefore, we can set the two equations equal to each other and solve for the acceleration:

T = Mgcos(theta) = 725.2N
725.2N = 74.0kg * a
a = 725.2N / 74.0kg = 9.8m/s^2

Therefore, the acceleration of the truck is 9.8m/s^2. It is important to note that this value is independent of the angle theta, as long as the truck is moving with constant acceleration. This is because the weight of the suspended mass and the tension in the string will always balance out and result in a net force of 725.2N acting on the truck.

In conclusion, by using the equation F=ma and considering the forces acting on the truck, we can determine the acceleration of the truck to be 9.8m/s^2.