A block of mass m is placed in a smooth-bored spring gun at the bottom of the in

Question

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. (Figure 1) . 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. Express the distance L in terms of x_c, k, m, g, mu, and theta. L=?

Explanation / Answer

Looks like you just didn't properly account for frictional energy loss The energy of the spring .5*k*(x_c)^2 will be converted to potential energy gain up the incline sin(th)*m*g*L and the loss due to friction. To compute friction, first determine the normal force N=cos(th)*m*g the frictional force is N*Mu or cos(th)*m*g*Mu and the work done is the force times displacement cos(th)*m*g*Mu*L since the friction works parallel to the surface of the incline, it works over the entire distance L Set up the equation .5*k*(x_c)^2= sin(th)*m*g*L+ cos(th)*m*g*Mu*L do some algebra .5*k*(x_c)^2= =m*g*L*(sin(th)+cos(th)*Mu) L= (.5*k*(x_c)^2)/ (m*g*(sin(th)+cos(th)*Mu)) j

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