IB Physics SL Review

Show that the maximum height of a fired projectile is given by vˆ2(sinˆ2x)/2g.

First, using vymax=u+ayt, set v to 0 (vymax=0). So, 0=v+gt. However, we need to use the y component, which is sinx times u. So, t=(sin x * u)/g. Now that we have t, we can use the equation sy=vyt+1/2gtˆ2 and substitute our equation in for t. Then, you should get the right answer.

Show that the range (total horizontal distance) of a projectile fired symmetrically is given by vˆ2sin(2x)/g.

Use the formula dx=vx * t. vx=cosx u. Substitute, and use our previously derived formula for t, but multiply everything by 2 in order to account for rise and fall. Substitue our newly multipled t in, and you should get the answer.

A person weighs 721 N. If the person sits in the middle of a hammock that is 3.0 m long and sags 1.0 m below the points of support, what force would be exerted by each of the two hammock ropes?

Using trig, we can calculate

A 3.0 kg mass and a 4.5 kg mass are hung on opposite ends of the same string across a frictionless pulley. As the system accelerates, what is the tension in the string?

1. Consider the whole system and calculate Fnet using the difference between the F2 and F1 (Force of smaller and larger masses respectively). Using the Fnet you just found, find the acceleration.

2. Now, you can zoom in and only consider one mass, because tension is the same everywhere. Because the system is aceclerating, Ft will be larger than Fg (Ft is working upwards). Ft-Fg=Fnet of the singular mass. Fg will be the weight of the mass, and Fnet will be 3 times 1.96 (the aceleration you found). Then, use simple algebra to find Ft.

A sphere of mass 5 kg moving at 4.00 m/s collides with an identifcal sphere that is at rest. The first sphere moves off at an angle of 60 degrees to the left of the original path, and the second sphere moves off in a direction 90 degrees to the right of the first sphere's final path. What are the the speeds of the two spheres as they seperate?

A 7.0 kg bowling ball moving at 6.0 m/s strikes a 1 kg bowling pin. If 10% of the initial kinetic energy of the bowling ball is lost in the collision, and all of the motion takes place along the same straight line, what are the velocies of the ball and the pin after the collision?

A 15.0 g rubber bullet travels at a velocity of 139 m/s, hits a stationary 8.4 kg concrete block rseting on a frictionless surface, and ricochets in the opposite direction with a speed of 98 m/s.

a) How fast will the concrete block be moving?

b) If the rubber bullet was in contact with the block for 5.3 ms, what was the average force exerted on the bullet by the block?

Batman, whose mass is 90 kg, is driving at 30 m/s towards Arkham Asylum. He spots a family of baby ducks crossing the road adn slams on his brake and avoids hitting the ducks. The Batmobile comes to a halt in 1.8 s. What force does Batman feel from his seeatbelt?

An 85 cm long pendulum with a 50 g mass on the end is pulled back until the string is horizontal to the countertop. The pendulum is then released. What is the tension in the string when the pendulum is at the bottom of its swing?

What is the height of the tallest loop the loop that a marble could successfully complete if rollled from an initial height of 42 cm along a ramp shaped as shown below

If a flying batman toy has a mass of 250 g flies in a circle with radius 75 cm and completes on circle every 0.9 seconds, what centripetal force is acting on the toy?

Methan moecules (CH4) are made of atoms of carbon (12C) and hydrgeon (1H). How many hydrogen atoms are in a 4.2 kg sample of methane?

1 mol of helium and 1 mol of gold have the same __.

number of molecules

If the density of gold (197 AU) is 19 g/cmˆ3, how many gold atoms are there in a gold ingot whose dimensions are 18 cm by 6.0 cm by 4.0 cm?

A planet has 36 times as much mass as a moon which orbits it. At some point P between the planet and the moon the net gravitational field is zero. If the distance from the center of the planet to the center of the moon is r, calculate the distance, in terms of r, you mnumst be away from the center of the planet to be at point P. 

Show that for orbital motion, tˆ2=4piˆ2rˆ3/GM.

Earth's mass and radius are 5.97 x 10ˆ24 kg and 6388 km, respectively .If the Earth's density were uniform (it's not, but lets assume), and you dug a hole halfway to the center of teh Earth, how much would you weigh at the bottom of the hole in  terms of your weight at the surface?

If c repreesnts the root mean square speed of particles in a sample, show that the average kinetic energy of the particles in that sample is given by Ek avg = 1/2mcˆ2. 

A hydraulic lift has two pistons, one with diameter 36 cm and the other with diameter 4.0 cm. How much force must be exerted on the smaller piston in order to lift a 190 kg mass placed on the large piston?