Answer:
A. 1.4 m/s to the left
Explanation:
To solve this problem we must use the principle of conservation of momentum. Let's define the velocity signs according to the direction, if the velocity is to the right, a positive sign will be introduced into the equation, if the velocity is to the left, a negative sign will be introduced into the equation. Two moments will be analyzed in this equation. The moment before the collision and the moment after the collision. The moment before the collision is taken to the left of the equation and the moment after the collision to the right, so we have:
where:
M = momentum [kg*m/s]
M = m*v
where:
m = mass [kg]
v = velocity [m/s]
where:
m1 = mass of the basketball = 0.5 [kg]
v1 = velocity of the basketball before the collision = 5 [m/s]
m2 = mass of the tennis ball = 0.05 [kg]
v2 = velocity of the tennis ball before the collision = - 30 [m/s]
v3 = velocity of the basketball after the collision [m/s]
v4 = velocity of the tennis ball after the collision = 34 [m/s]
Now replacing and solving:
(0.5*5) - (0.05*30) = (0.5*v3) + (0.05*34)
1 - (0.05*34) = 0.5*v3
- 0.7 = 0.5*v
v = - 1.4 [m/s]
The negative sign means that the movement is towards left
Answer:
μsmín = 0.1
Explanation:
- There are three external forces acting on the riders, two in the vertical direction that oppose each other, the force due to gravity (which we call weight) and the friction force.
- This friction force has a maximum value, that can be written as follows:
where μs is the coefficient of static friction, and Fn is the normal force,
perpendicular to the wall and aiming to the center of rotation.
- This force is the only force acting in the horizontal direction, but, at the same time, is the force that keeps the riders rotating, which is the centripetal force.
- This force has the following general expression:
where ω is the angular velocity of the riders, and r the distance to the
center of rotation (the radius of the circle), and m the mass of the
riders.
Since Fc is actually Fn, we can replace the right side of (2) in (1), as
follows:
- When the riders are on the verge of sliding down, this force must be equal to the weight Fg, so we can write the following equation:
- (The coefficient of static friction is the minimum possible, due to any value less than it would cause the riders to slide down)
- Cancelling the masses on both sides of (4), we get:
- Prior to solve (5) we need to convert ω from rev/min to rad/sec, as follows:
- Replacing by the givens in (5), we can solve for μsmín, as follows:
Answer:
15.8 m/s
Explanation:
The following data were obtained from the question:
Initial velocity (u) = 32 m/s.
Acceleration (a) = – 1.5 m/s²
Time (t) = 10.8 s.
Final velocity (v) =?
Acceleration is simply defined as the rate of change of velocity with time. Mathematically, it is expressed as:
Acceleration (a) = [final velocity (v) – initial velocity (u)] / time (t)
a = (v – u) /t
With the above formula, we can obtain the final velocity of go-cart driver as follow:
Initial velocity (u) = 32 m/s.
Acceleration (a) = – 1.5 m/s²
Time (t) = 10.8 s.
Final velocity (v) =?
a = (v – u) /t
– 1.5 = (v – 32) / 10.8
Cross multiply
(v – 32) = –1.5 × 10.8
v – 32 = – 16.2
Collect like terms
v = – 16.2 + 32
v = 15.8 m/s
Therefore, the final velocity of go-cart driver is 15.8 m/s.
Answer:
Explanation:
The water moving into the high tide areas has moved out of the low tide areas. Water is incompressible.
If you have ever lived in Chicago, then the answer might very well be C.
Newton's Second law states F = ma. This problem has nothing to do with acceleration.
Newton's Third law is the familiar action/reaction law. If the poles are anchored well enough and have a flexural strength greater than the tension exerted on them by the wire; then D is just.
That leaves B. There's no problem all we have to do is to increase the horizontal tension in the cable.
