Answer:
101.54m/h
Explanation:
Given that the buses are 5mi apart, and that they are both driving at the same speed of 55m/h, rate of change of distance can be determined using differentiation as;
Let l be the be the distance further away at which they will meet from the current points;
#The speed toward each other.
Hence, the rate at which the distance between the buses is changing when they are 13mi apart is 101.54m/h
Answer:
W = 55.12 J
Explanation:
Given,
Natural length = 6 in
Force = 4 lb, stretched length = 8.4 in
We know,
F = k x
k is spring constant
4 = k (8.4-6)
k = 1.67 lb/in
Work done to stretch the spring to 10.1 in.
W = 55.12 J
Work done in stretching spring from 6 in to 10.1 in is equal to 55.12 J.
1) 4 forces
2) 165 N
3) 225 N
Explanation:
1)
There are in total 4 forces acting on the bicylist:
- The gravitational force on the byciclist, acting vertically downward, of magnitude , where m is the mass of the bicyclist and g is the acceleration due to gravity
- The normal force exerted by the floor on the bicyclist and the bike, N, vertically upward, and of same magnitude as the gravitational force
- The force of push F, acting horizontally forward, given by the push exerted by the bicylist on the pedals
- The air drag, R, of magnitude R = 60.0 N, acting horizontally backward, in the direction opposite to the motion of the bicyclist
2)
The magnitude of the net force on the bicyclist can be calculated by considering separately the two directions.
- Along the vertical direction, we have the gravitational force (downward) and the normal force (upward); these two forces are equal in magnitude, since the acceleration of the bicyclist along this direction is zero, therefore the net force in this direction is zero.
- Along the horizontal direction, the two forces (forward force of push and air drag) are balanced, since the acceleration is non-zero, so we can use Newton's second law of motion to find the net force on the bicylist:
where
is the net force
m = 75.0 kg is the mass of the bicyclist
is its acceleration
Solving, we find the net force:
3)
In this part, we basically want to find the forward force of push, F.
We can rewrite the net force acting on the bicyclist as
where:
F is the forward force of push
R is the air drag
We know that:
is the net force on the bicyclist
R = 60.0 N is the magnitude of the air drag
Therefore, by re-arranging the equation, we can find the force generated by the bicylicst by pedaling: