Time taken for an object to slide down a plane given μ, s and θ

[PhysicsThrow]

Homework Statement

Find the time taken for an object to slide down an inclined plane given the coefficient of friction, length of slope and angle of incline.
The coefficient of friction is 0.3.
The angle of incline is 30°.
The length of the slope is 6m.

Homework Equations

F=μN
F=(mg)sin(30)
N=(mg)cos(30)
F=ma

s=ut+1/2at²?

The Attempt at a Solution

Completely stuck. I assume I must calculate the mass of the object first? Using F=μN some how? Then I can calculate the acceleration of the object with F=ma? Then I can find the time taken to slide down with s=ut+1/2at²?

 

[Doc Al]

I assume I must calculate the mass of the object first? Using F=μN some how?

You won't need the mass. But you will need the net force. (Symbolically, not with numbers at this point.)

Then I can calculate the acceleration of the object with F=ma?

Yes, where F is the net force.

Then I can find the time taken to slide down with s=ut+1/2at²?

Yep.

 

[PhysicsThrow]

You won't need the mass. But you will need the net force. (Symbolically, not with numbers at this point.)

Ahah! I think I have it then!

ma = mg(sin(30)+-0.30cos(30)
ma = m*2.36
so, a = 2.36

 

[Doc Al]

Ahah! I think I have it then!

ma = mg(sin(30)+-0.30cos(30)
ma = m*2.36
so, a = 2.36

Good!

 

[Nickie]

I would approach this problem by first identifying the known variables and the relevant equations that can be used to solve for the unknown variable, which in this case is time (t). The known variables are the coefficient of friction (μ= 0.3), the length of the slope (s= 6m), and the angle of incline (θ= 30°). The relevant equations are F=μN, F=(mg)sin(θ), N=(mg)cos(θ), and s=ut+1/2at^2.

To solve for time, we need to first calculate the force of friction (F) using the equation F=μN. To do this, we need to find the normal force (N) acting on the object. We can find N by using the equation N=(mg)cos(θ), where m is the mass of the object and g is the acceleration due to gravity (9.8 m/s^2). We can then substitute this value for N into the equation F=μN to solve for F.

Next, we can calculate the net force (Fnet) acting on the object by adding the force of gravity (mg) acting downwards and the force of friction (F) acting in the opposite direction. The net force can be calculated using the equation Fnet=mg-F.

Since we know that the acceleration of the object (a) is equal to the net force divided by the mass, we can now solve for a using the equation F=ma. Once we have calculated the acceleration, we can use the equation s=ut+1/2at^2 to solve for time (t).

In summary, the steps to solve for the time taken for an object to slide down an inclined plane would be:

1. Calculate the normal force (N) using the equation N=(mg)cos(θ).
2. Calculate the force of friction (F) using the equation F=μN.
3. Calculate the net force (Fnet) using the equation Fnet=mg-F.
4. Calculate the acceleration (a) using the equation F=ma.
5. Finally, use the equation s=ut+1/2at^2 to solve for time (t).

I hope this helps in solving the problem. Remember to always identify your known variables and use relevant equations to solve for the unknown variable.