Please help with what equations to use for displacement and work for the the tale below. And how to solve problems thank you.

Link for questions are below

Work and Energy Lab Online

Purpose:

To determine the effect of the angle of an inclined plane upon the amount of force and the amount of work done when pulling a cart up an inclined plane at a constant speed and to the same height. To analyze the relationship between kinetic energy, potential energy, and total energy. Observe the difference in conservative and non-conservative forces.

Equipment:

• https://www.physicsclassroom.com/Physics-Interactives/Work-and-Energy/Its-All-Uphill/Its-All-Uphill-Interactive
• https://phet.colorado.edu/sims/html/energy-skate-park/latest/energy-skate-park_en.html

Discussion:

One of the most important concepts to understanding the universe is the conservation of energy, "energy can not be created or destroyed, just transformed". This universal law must hold true for all types of energy. This lab deals specifically with that of mechanical energy. We have defined that mass in motion has Kinetic Energy. The equation for Kinetic Energy is

K=1/2mv2 (1)

Where m is mass and v is the speed squared. While under the influence of gravity near a planet's surface we have derived gravitational Potential Energy

Ug?=mgh (2)

Where m is mass, g is the free-fall acceleration, and h is the vertical height. Which is dependent upon the height the mass is above the zero point, we generally determine this point to be the surface of the planet. With an object undergoing conservative forces, the transformation of energy is ideal, with one energy flowing into the next. This process could be repeated endlessly, but other forces prevent this. Work is the ability for a force to change the energy of a system. Forces can be considered conservative or non-conservative. Forces that are path independent are considered conservative forces. These forces if we include them in our system are able to be represented as a potential energy, as they will oscillate. Non-conservative forces are path dependent. As a force is applied to an object we can calculate its work, the change in energy of the system as

W=Fdcos?? (3)

Where F is the applied force, d is the displacement, and the angle ? is the angle between the force and displacement vectors.

Procedure:

1. Open the Its-All-Uphill activity from Physicsclassroom.com
2. Click the begin activity button.
3. Select a mass from one of the three choices. Record your value: Mass choose is 2
4. Click the 30 angle.
5. The cart is going to be pulled up at a constant speed, to reach a vertical height of 1 m. You will need to measure the displacement along the distance of the ramp.
6. Tap the Run Trial button. The force required to pull the cart at a constant speed is displayed on the screen; record in Data Table 1.
7. The displacement from the starting position to the final position can be measured using the ruler; record in Data Table 1. (Note that the table lists meters as the unit but the ruler is in cm.) The force and the displacement vectors are both directed parallel to the inclined plane. Use the force and displacement to calculate the work done.
8. Repeat the procedure for all angles. Show your calculation for at least 1 trial.

Table 1

Angle (Deg)	Force (N)	Displacement (m)	Work (J)
30	9.8 N
40	12.6 N
50	15.0 N
60	17.0 N
70	18.4 N
80	19.3 N
90	19.6 N

Question 1: Construct plots of the force and work as a function of the incline angle. Include the line of best fit through the data. You can use Figure 1.

Figure 1

Force (N) Angle (Deg, " ) 50 40 30 Work (J) 20 10 10 20 30 40 50 60 70 80 90 Angle (Deg, " )