End of the semester, working on the final review...

I have a couple of questions I am stuck on right now. My notes on these questions seem to have vanished into the void...

1. "A 2.0kg puck travelling due east at 2.5m/s collides with a 1.0kg puck travelling due south at 3.0m/s. They stick together on impact. What is the resultant direction of the combined pucks?"

Now, I added up the vectors and know that they will be travelling S of E, but don't know how to find the degrees?

2. "A mass suspended by a string is held 24 degrees from vertical by a forse of 13.8N. Find the mass."

My FBD has a mass with an Ft, a force of 13.8N pulling to the right, and an Fg heading straight down. My Fg=mg, but now I am sort of stuck.

Please help!:)

1. The east (e) and south (s) momentum vectors remain the same, and the velocity ratio of those components is the same as the momentum ratio.

(MVs)/MVe) = Vs/Ve = (1x3)/(2x2.5) = 0.6

The final angle, measured south of east is arctangent 0.6 = 31.0 degrees

The final speed is
|V| = (Final momentum)/m
sqrt(3^2 + 5^2)/3 = 1.94 m/s

2. Let Ft be the string tension force. I will assume that the force Fh = 13.8 N that holds it at that angle is horizontal ("to the right"). g, h and t are subscripts, not variables.
The FBD tells you that

Ft sin 24 = Fh = 13.8
Ft cos 24 = Fg
Take the ratio to eliminate Ft.
tan 24 = 13.8/Fg
Fg = 31.0 Newtons
Since Fg is the weight (M*g), divide by g = 9.8 m/s^2 to get the mass M.

Sure, I can help you with these questions!

1. To find the resultant direction of the combined pucks, you can use vector addition. Since the pucks stick together after the collision, the resultant velocity will be equal to their combined momentum divided by their combined mass.

First, find the momentum of each puck. Momentum (p) is given by the product of mass (m) and velocity (v): p = mv.

For the first puck:
Mass (m1) = 2.0 kg
Velocity (v1) = 2.5 m/s
Therefore, momentum of the first puck (p1) = (2.0 kg) * (2.5 m/s) = 5.0 kg·m/s

For the second puck:
Mass (m2) = 1.0 kg
Velocity (v2) = 3.0 m/s
Therefore, momentum of the second puck (p2) = (1.0 kg) * (3.0 m/s) = 3.0 kg·m/s

Now, add the two momenta together to find the total momentum of the system:
Total momentum (ptotal) = p1 + p2 = 5.0 kg·m/s + 3.0 kg·m/s = 8.0 kg·m/s

Since the pucks stick together, their combined mass is the sum of their individual masses:
Combined mass (m_combined) = m1 + m2 = 2.0 kg + 1.0 kg = 3.0 kg

Finally, divide the total momentum by the combined mass to find the resultant velocity:
Resultant velocity (v_resultant) = ptotal / m_combined = (8.0 kg·m/s) / (3.0 kg) ≈ 2.67 m/s

Now, to determine the resultant direction, you can use trigonometry. Since the pucks were initially traveling due east and due south, the resultant velocity will be south of east, forming a right triangle. You can use the tangent function to find the angle:

tangent(angle) = opposite side / adjacent side
tangent(angle) = v_resultant / 2.5 m/s

Now you can find the angle:
angle = arctan(v_resultant / 2.5 m/s)

Just plug in the value you calculated for the resultant velocity and solve for the angle using a calculator or trigonometric functions on a computer.

2. To find the mass of something when given an angle and a force, we can use the concept of tension and the equation for equilibrium of forces.

In this case, you have a mass (m) suspended by a string, making an angle (θ) of 24 degrees with the vertical. The force pulling horizontally is 13.8 N (the tension in the string).

Start by drawing a free-body diagram (FBD) of the mass. You correctly identified that there is the tension force (F_tension) going to the right and the force of gravity (F_gravity) going straight down.

The force of gravity (F_gravity) can be calculated using the equation F_gravity = m * g, where g is the acceleration due to gravity (approximately 9.8 m/s^2). In this case, F_gravity acts in the downward direction and can be broken into two components: one along the vertical axis and one along the horizontal axis. The component along the horizontal axis does not affect the equilibrium, so we only need to consider the vertical component.

The vertical component of the force of gravity (F_gravity-vertical) can be calculated using the equation F_gravity-vertical = F_gravity * sin(θ).

Next, we apply the concept of equilibrium, which means that the sum of all forces in both the horizontal and vertical directions should be zero.

In the horizontal direction:
F_tension = 0 (since there are no other forces acting horizontally)

In the vertical direction:
F_tension - F_gravity-vertical = 0

Now, substitute the values:
F_tension - (m * g * sin(θ)) = 0

You are given the force of tension (F_tension) as 13.8 N and the angle (θ) as 24 degrees. You need to solve for the mass (m).

m * g * sin(θ) = F_tension
m * (9.8 m/s^2) * sin(24 degrees) = 13.8 N

Now, divide both sides by (9.8 m/s^2) * sin(24 degrees) to solve for m:
m = 13.8 N / (9.8 m/s^2 * sin(24 degrees))

Plug in the values and calculate using a calculator or trigonometric functions on a computer to find the mass.

I hope this helps you solve the questions! Let me know if you have any further questions.