Translational Motion

Question 1

Scalar vs Vector

Answer 1

• Scalar: without direction. For example, length, time, mass.
• Vector: with direction. For example, displacement, acceleration, force.

Question 2

Axis-Vector components

Question 3

Vector-Vector components

Question 4

Gravity components on slope

Question 5

Speed vs Velocity

Answer 5

• Speed: scalar, no direction, rate of change in distance.
• Velocity: vector, has direction, rate of change in displacement.

Question 6

Instantaenous speed vs Instantaneous velocity

Answer 6

SPEED: Instantaneous speed is the speed at an instant (infinitesimal time interval). Instantaneous speed equals instantaneous velocity in magnitude.

VELOCITY: Instantaneous velocity is the velocity at an instant (infinitesimal time interval). Instantaneous velocity has a direction, instantaneous speed does not. The direction of instantaneous velocity is tangent to the path at that point.

Question 7

Add the following vectors and determine the resultant.:

5.0 m/s, 45 deg and 2.5 m/s, 135 deg

Answer 7

5.0 m/s, 45 deg+ 2.5 m/s, 135 deg= 5.59 m/s, 71.6 deg

MAGNITUDE: 5² + 2.5² = 31.25 whose square root is 5.59

DIRECTION: The x-component of the resultant vector is 5cos(45) + 2.5cos(135) = 1.77 and the y-component of the resultant vector is 5sin(45) + 2.5sin(135) = 5.30. Then, you take the tan^-1(5.30/1.77) which is 71.6 degrees.

Question 8

Add the following vectors and determine the resultant.

3.0 m/s, 45 deg and 5.0 m/s, 135 deg and 2.0 m/s, 60 deg

Answer 8

MAGNITUDE:

x component: 3cos(45) + 5cos(135) + 2cos(60) = -0.414

y component: 3sin(45) + 5sin(45) + 2sin(60) = 7.389

Finding the square root of the sums of the components: 7.401

DIRECTION: tan-1(7.389/-0.414) = -86.79 + 180 = 93.21.

Question 9

What are the FOUR equations at constant acceleration?

Question 10

What happens to the speed at terminal velocity?

Answer 10

At terminal velocity, weight = friction, so the net force is 0. Thus, the acceleration is 0. So, the speed stays constant at terminal velocity.

Question 11

What will happen to the acceleration with air resistance?

Answer 11

• The acceleration is no longer constant - it will decrease with time until it gets to zero at terminal velocity.
• When there’s air resistance, the acceleration will decrease because the force (weight - resistance) is decreasing due to increasing resistance or friction at higher speeds.

Question 12

What do you use to find the time that a projectile is in air?

Answer 12

Use the vertical component only.

Question 13

How do you find how far a projectile traveled?

Answer 13

First get the time in the air by the vertical component. Then use the horizontal component’s speed * time of flight

Question 14

Equation for uniform circular motion

Question 15

A pool ball leaves a 0.60-meter high table with an initial horizontal velocity of 2.4 m/s. Predict the time required for the pool ball to fall to the ground and the horizontal distance between the table’s edge and the ball’s landing location.

Answer 15

y = -0.60 m = (0 m/s)•t + 0.5•(-9.8 m/s/s)•t²

t = 0.350 s

x = (2.4 m/s)•(0.3499 s) + 0.5•(0 m/s/s)•(0.3499 s)²

x = 0.84 m