Instead of lifting the box straight up, suppose you push it up a 1.0-m-high ramp that makes a 30 ∘ degree angle with the horizontal, as shown in (Figure 1). Being clever, you choose a ramp with no friction. How much force is required to push the box straight up the slope at a constant speed?

Describe the path of a ray that approaches a mirror parallel to the principal axis.

Which additional product balances the reaction h2so4 + 2naoh → na2so4 + 2h2o 2oh h2o2 h3o

In an old-fashioned amusement park ride, passengers stand inside a 3.0-m-tall, 5.0-m-diameter hollow steel cylinder with their backs against the wall. the cylinder begins to rotate about a vertical axis. then the floor on which the passengers are standing suddenly drops away! if all goes well, the passengers will “stick” to the wall and not slide. clothing has a static coefficient of friction against steel in the range 0.60 to 1.0 and a kinetic coefficient in the range 0.40 to 0.70. part a what is the minimum rotational frequency, in rpm, for which the ride is safe? express your answer using two significant figures. f f = rpm