Question

An 8.5 kg crate is pulled 5.1 m up a 30 degree incline by a rope angled 17 degrees above the incline. The tension in the rope is 140 N and the crate's coefficient of kinetic friction on the incline is 0.27.1.) How much work is done by (a) tension, by (b) gravity, and by (c) the normal force?2. ) What is the increase in thermal energy of the crate and incline?

Answer 1

1. a
`W_t=746.63 J`

b
`E_p=212.415 J`

c
`W_n=183.96J`

2.
`T_e=99.71J`

Step-by-step explanation:

a). The work done by the tension is:

`W_t=T*dt`

`dt=(5.1)/(cos(17))`

`W_t=140N*(5.1)/(cos(17))`

`W_t=746.63 J`

b). The work done potential of gravity

`E_p=m*g*h`

`h=5.1*sin(17)`

`E_p=8.5kh*9.8*5.1*sin(30)`

`E_p=212.415 J`

c). The work done by the normal force

`W_n=N*d_n`

`d_n=5.1*sin(30)=2.55`

`W_n=8.5kg*9.8*cos(30)*2.55`

`W_n=183.96J`

2. The increase in thermal energy is:

`T_e=F*d`

`F_k=u_k*m*g=0.271*8.5kg*9.8*cos(30)`

`F_k=19.5N`

`T_e=19.55*5.1m`

`T_e=99.71J`