27. The equation e = 1200 + 11t represents your elevation e in feet for each minute t you hike from a trailhead.
1 answer:
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Answer:
(A) 374.4 J
(B) -332.8 J
(C) 0 J
(D) 41.6 J
(E) 351.8 J
Explanation:
weight of carton (w) = 128 N
angle of inclination (θ) = 30 degrees
force (f) = 72 N
distance (s) = 5.2 m
(A) calculate the work done by the rope
- work done = force x distance x cos θ
- since the rope is parallel to the ramp the angle between the rope and
the ramp θ will be 0
work done = 72 x 5.2 x cos 0
work done by the rope = 374.4 J
(B) calculate the work done by gravity
- the work done by gravity = weight of carton x distance x cos θ
- The weight of the carton = force exerted by the mass of the carton = m x g
- the angle between the force exerted by the weight of the carton and the ramp is 120 degrees.
work done by gravity = 128 x 5.2 x cos 120
work done by gravity = -332.8 J
(C) find the work done by the normal force acting on the ramp
- work done by the normal force = force x distance x cos θ
- the angle between the normal force and the ramp is 90 degrees
work done by the normal force = Fn x distance x cos θ
work done by the normal force = Fn x 5.2 x cos 90
work done by the normal force = Fn x 5.2 x 0
work done by the normal force = 0 J
(D) what is the net work done ?
- The net work done is the addition of the work done by the rope, gravitational force and the normal force
net work done = 374.4 - 332.8 + 0 = 41.6 J
(E) what is the work done by the rope when it is inclined at 50 degrees to the horizontal
- work done by the rope= force x distance x cos θ
- the angle of inclination will be 50 - 30 = 20 degrees, this is because the ramp is inclined at 30 degrees to the horizontal and the rope is inclined at 50 degrees to the horizontal and it is the angle of inclination of the rope with respect to the ramp we require to get the work done by the rope in pulling the carton on the ramp
work done = 72 x 5.2 x cos 20
work done = 351.8 J
1) Gravitational potential energy
In fact, gravitational potential energy is given by:
where m is the mass of the roller coaster, g is the gravitational acceleration and h is the heigth. Therefore, when the roller coaster goes uphill, the height h increases and the roller coaster gains gravitational potential energy.
2) The relationship between potential and kinetic energy is:
where ME is the total mechanical energy, KE is the kinetic energy, GPE is the gravitational potential energy. Since the value of ME is constant (when no friction is present), this means that when KE increases, GPE decreases, and vice-versa.
3) If friction is removed from the track, the roller coaster would move forever. In fact, in the equation written in part 2), ME is constant only in case there is no friction - when friction is present, part of the energy is lost due to the friction, so the total ME available decreases little by little until it becomes zero, and the roller coaster cannot move anymore.
4) It matters because it affects the magnitude of the friction. In fact, friction is given by
where is the coefficient of friction, m is the mass ,and g the gravitational acceleration. When the number of carts is increased, the mass increases, therefore the friction increases as well.