Respuesta :
Answer:
a) [tex]W_g =61.25J[/tex]
b) [tex]W_k = -46.25J[/tex]
c) [tex]W_N = 0[/tex]
d) [tex]W_g[/tex] would be the same.
[tex]W_k[/tex] would decrease.
[tex]W_N[/tex] would be the same.
Explanation:
a) On an inclined plane the force of gravity is the sine component of the weight of the block.
[tex]F_g = mg\sin(\theta) = 5(9.8)\sin(30^\circ)\\W_g = F_g x = 5(9.8)\sin(30^\circ)2.5 = 61.25J[/tex]
b) The friction force is equal to the normal force times coefficient of friction.
[tex]F_k = -mg\cos(\theta)\mu_k = -5(9.8)cos(30^\circ)0.436 = -18.5 N\\W_k = -F_kx = -46.25J[/tex]
c) The work done by the normal force is zero, since there is no motion in the direction of the normal force.
d) The relation between the vertical height and the distance on the ramp is
[tex]h = x\sin(\theta)[/tex]
According to this relation, the work done by the gravity wouldn't change, since the force of gravity includes a term of [tex]x\sin(\theta)[/tex].
The work done by the friction force would decrease, because both the cosine term and the distance on the ramp would decline.
The work done by the normal force would still be zero.
(a) The work done by force of gravity on the block during the motion is 61.25 J.
(b) The work done by the friction force between block and incline is -46.3 J.
(c) The work done by the normal force is zero.
(d) A steeper angle means that the angle of inclination to the horizontal will increase. The work done by gravity will increase and the work done by friction will reduce.
The given parameters;
- mass of the block, 5 kg
- distance traveled by the block, d = 2.5 m
- inclination of the plane = θ = 30⁰
- coefficient of kinetic friction, μ = 0.436
(a) The work done by force of gravity is calculated as follows;
[tex]W = mgsin \theta \times d\\\\W = (5\times 9.8 \times sin(30)) \times 2.5\\\\W = 61.25 \ J[/tex]
(b) The work done by the friction force between block and incline is calculated as follows;
[tex]W = -F_k d\\\\W =-(\mu mgcos\ \theta) \times d\\\\W = -(0.436 \times 5 \times 9.8 \times cos(30)) \times 2.5\\\\W = -46.3\ J[/tex]
(c) The work done by the normal force is zero since there is no motion in vertical direction.
(d) A steeper angle means that the angle of inclination to the horizontal will increase. The work done by gravity will increase since sine of the angle increases when the angle increases. Also, the work done by friction will reduce because cosine of angle decreases with increases in the value of the angle of inclination.
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