please solve this problems Suppose the inclined plane is tip

please solve this problems...

Suppose the inclined plane is tipped so it makes an angle theta = 8.120degree plusminus 0.024degree with the horizontal. The 0 cm mark is at the bottom. The lower photogate is at the 20.400 cm plusminus 0.150 cm mark, and the upper photogate is at the 53.300 cm plusminus 0.169 cm mark along the track, Assume - The potential energy is zero at the lower photogate. - The total mass of the cart is 852.0 g plusminus 25.4 g. - The track is totally frictionless - Use g = 9.802 plusminus 0.005 m/s^2. a) Find each quantity with its uncertainty: - the height of the upper photogate above the zero energy point. t m - the potential energy of the cart at the upper photogate. b) Suppose the cart is released at rest at some point above the upper photogate, and it passes through the upper photogate at speed 0.655 m/s In procedure 2: suppose the inclined plane is tipped so it makes an angle theta = 8.120degree plusminus 0.024degree with the horizontal. The 0 cm mark is at the bottom. The lower photogate is at the 20.400 cm plusminus 0.150 cm mark, and the upper photogate is at the 53.300 cm plusminus 0.169 cm mark along the track, Assume - The potential energy is zero at the lower photogate. - The total mass of the cart is 852.0 g plusminus 25.4 g. - The track is totally frictionless - Use g = 9.802 plusminus 0.005 m/s^2. a) Find each quantity with its uncertainty: - the height of the upper photogate above the zero energy point. t m - the potential energy of the cart at the upper photogate. 0.022 m/s. Find each quantity with its uncertainty: - the kinetic energy of the cart at the upper photogate.

Solution

H = Upper Photogate - Lower Photogate

H = 53.300 +- .169 - ( 20.400 +- 0.150)

(A ± A) - (B ± B) = (A - B) ± (A + B)

H = 0.329 +- ( 0.00319) m

For Multiplication

(A ± A) x (B ± B) = (A x B) ± (A + B)

U = m*g*h = ( .852 +-25.4/8.52) * (9.802 +- .5/9.802) *  (0.329 +- ( 0.319/.329))

Adding the unceratinites we got it to be 4 %, hence finding 4 % of 2.747 to be 0.109.

U = 2.747 +- (0.109) J