please label answers thanks in advance friends 1. A cart for hauling ore out of
ID: 1283702 • Letter: P
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please label answers thanks in advance friends
1. A cart for hauling ore out of a gold mine has a mass of 413 kg, including its load. The cart runs along a straight stretch of track that is sloped 4.27 degree from the horizontal. A donkey, trudging along and to the side of the track, has the unenviable job of pulling the cart up the slope with a 374-N force for a distance of 129 m by means of a rope that is parallel to the ground and makes an angle of 13.9 degree with the track. The coefficient of friction for the cart's wheels on the track is 0.0151. Use g = 9.81 m/s^2. Find the work that the donkey performs on the cart during this process. Find the work that the force of gravity performs on the cart during the process. Calculate the work done on the cart during the process by friction. 2. A block of mass m = 4.55 kg slides along a horizontal table with speed vo = 7.50 m/s. At x = 0 it hits a spring with spring constant k = 64.00 N/m and it also begins to experience a friction force. The coefficient of friction is given by mu = 0.200. How far has the spring compressed by the time the block first momentarily comes to rest?Explanation / Answer
1)Work by donkey=FdCos(theta)=374*129*Cos(13.9)=46833J
Work by gravity=-mgh=-413*9.81*129Sin(4.27)=-38915J
Work by friction=-umgCos(theta)*d=-0.0151*413*9.81*Cos(4.27)*129=-7870J
2)Conserving energy,
0.5mv^2=0.5kx^2+umgd
0.5*4.55*7.5^2=0.5*64*x^2+0.2*4.55*9.81*x
Solving for x,
x=1.87m
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