How Far Does a Block Travel Up an Incline After Shooting from a Spring Gun?

[MAPgirl23]

A block of mass m is placed in a smooth-bored spring gun at the bottom of the incline so that it compresses the spring by an amount x_c. The spring has spring constant k. The incline makes an angle theta with the horizontal and the coefficient of kinetic friction between the block and the incline is mu. The block is released, exits the muzzle of the gun, and slides up an incline a total distance L.

Find L, the distance traveled along the incline by the block after it exits the gun. Ignore friction when the block is inside the gun. Also, assume that the uncompressed spring is just at the top of the gun (i.e., the block moves a distance x_c while inside of the gun). Use g for the magnitude of acceleration due to gravity.

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mg = -Force of gravity*sin(theta)= -mgsin(theta)
a = -gsin(theta) where it slides down
height = (x_c+L)sin(theta)
F = 0.5*k*x^2

but how do I find L?

 

[hotvette]

I believe you left out the effect of the kinetic friction. On a problem like this it's probably best to start from the basics - draw a free body diagram, label the forces, write F=ma in the coordinate directions, and solve from there.

 

[MAPgirl23]

mg = -Force of gravity*sin(theta)-mu_k= -mgsin(theta)-mu_k

 

[hotvette]

If I understand the problem correctly, the mass enters the incline with an initial velocity, so you'll need the full equation of motion. So, I would think of this as 2 separate problems. The first, to find out the velocity of the mass as it exits the gun (i.e. enters the incline). The second problem is a mass sliding up an incline with an initial velocity subject to friction and gravity. By the way, if mu_k is the coefficient of friction, it need to be multiplied by a normal force N to be a valid force.

The first problem could be tricky. My guess is that using energy equations is probably the must fruitful approach.